Competing Magnetic Phases on a Kagomé Staircase

We present thermodynamic and neutron data on ${\mathrm{N}\mathrm{i}}_3{\mathrm{V}}_2{\mathrm{O}}_8$, a spin-1 system on a kagomé staircase. The extreme degeneracy of the kagomé antiferromagnet is lifted to produce two incommensurate phases at finite $T$—one amplitude modulated, the other helical—plus a commensurate canted antiferromagnet for $T\to 0$. The $H\mathrm{\text{−}}T$ phase diagram is described by a model of competing first and second neighbor interactions with smaller anisotropic terms. $\mathrm{N}{\mathrm{i}}_3{\mathrm{V}}_2{\mathrm{O}}_8$ thus provides an elegant example of order from subleading interactions in a highly frustrated system.

Figure 1

(a) Structure of NVO, showing the cross-tie ${\mathrm{N}\mathrm{i}}_c$ [blue (gray)] and spine ${\mathrm{N}\mathrm{i}}_s$ [red (black)] sites. (b)–(c) indicate the spin structures in the IC phases. $+/-$ indicate spin components along $\mathbf{b}$. Symbol sizes scale with the dipole moment. (d) indicates the symmetry of the C′ structure. Spin canting has been exaggerated for clarity and the relative symbol sizes for spine and cross-tie spins are not to scale. Subsequent layers are displaced by $(\mathbf{a}+\mathbf{b})/2$ with spine spins satisfying Eq. (1). Lattice parameters serve as axis length units.

Figure 2

Phase diagram for NVO as a function of temperature and magnetic field applied along the three principal crystallographic directions. For $\mathbf{H}\parallel \mathbf{c}$ no true phase boundary separates the P and C phases. White areas were not probed.

Figure 3

(a) Specific heat of NVO, in zero field and for $\mathbf{H}\parallel \mathbf{c}$. (b) Longitudinal magnetization versus $T$ for $H=0.1\mathrm{T}$ along the three principal crystallographic directions. (c) Integrated intensity of commensurate and incommensurate magnetic Bragg peaks at $\mathbf{Q}=(110)$ and $(1\pm q/a^{*},1,0)$, respectively. (d) Temperature dependence of the incommensurate magnetic wave vector. In the C and C′ phases, we believe the incommensurate peak reflects a metastable minority phase as it is only present after cooling through the HTI and LTI phases and can be fully suppressed by field cycling.